Question

Question 5 (iv)
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

1825

Answer 1

1825

$\begin{array}{cc}& 42\\ 4& \overline{18}\overline{25}\\ & -16\\ 82& 225\\ & -164\\ & 61\end{array}$

Since remainder is 61. Therefore ${42}^2<1825$

Next perfect square number ${43}^2=1849$

Hence, number to be added = 1849 – 1825 = 24

$\therefore 1825+24=1849$

Hence, the square root of 1849 is 43.